1,749 research outputs found
On the Two-Dimensional Knapsack Problem for Convex Polygons
We study the two-dimensional geometric knapsack problem for convex polygons. Given a set of weighted convex polygons and a square knapsack, the goal is to select the most profitable subset of the given polygons that fits non-overlappingly into the knapsack. We allow to rotate the polygons by arbitrary angles. We present a quasi-polynomial time O(1)-approximation algorithm for the general case and a polynomial time O(1)-approximation algorithm if all input polygons are triangles, both assuming polynomially bounded integral input data. Also, we give a quasi-polynomial time algorithm that computes a solution of optimal weight under resource augmentation, i.e., we allow to increase the size of the knapsack by a factor of 1+? for some ? > 0 but compare ourselves with the optimal solution for the original knapsack. To the best of our knowledge, these are the first results for two-dimensional geometric knapsack in which the input objects are more general than axis-parallel rectangles or circles and in which the input polygons can be rotated by arbitrary angles
Integer Points in Knapsack Polytopes and s-covering Radius
Given an integer matrix A satisfying certain regularity assumptions, we
consider for a positive integer s the set F_s(A) of all integer vectors b such
that the associated knapsack polytope P(A,b)={x: Ax=b, x non-negative} contains
at least s integer points. In this paper we investigate the structure of the
set F_s(A) sing the concept of s-covering radius. In particular, in a special
case we prove an optimal lower bound for the s-Frobenius number
2D multi-objective placement algorithm for free-form components
This article presents a generic method to solve 2D multi-objective placement
problem for free-form components. The proposed method is a relaxed placement
technique combined with an hybrid algorithm based on a genetic algorithm and a
separation algorithm. The genetic algorithm is used as a global optimizer and
is in charge of efficiently exploring the search space. The separation
algorithm is used to legalize solutions proposed by the global optimizer, so
that placement constraints are satisfied. A test case illustrates the
application of the proposed method. Extensions for solving the 3D problem are
given at the end of the article.Comment: ASME 2009 International Design Engineering Technical Conferences &
Computers and Information in Engineering Conference, San Diego : United
States (2009
Exhaustive Search-based Model for Hybrid Sensor Network
A new model for a cluster of hybrid sensors network with multi sub-clusters
is proposed. The model is in particular relevant to the early warning system in
a large scale monitoring system in, for example, a nuclear power plant. It
mainly addresses to a safety critical system which requires real-time processes
with high accuracy. The mathematical model is based on the extended
conventional search algorithm with certain interactions among the nearest
neighborhood of sensors. It is argued that the model could realize a highly
accurate decision support system with less number of parameters. A case of one
dimensional interaction function is discussed, and a simple algorithm for the
model is also given.Comment: 6 pages, Proceeding of the International Conference on Intelligent &
Advanced Systems 2012 pp. 557-56
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